# 110110 - 1 CHM3400 Lecture 3 – Jan 10 Maxwell...

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Unformatted text preview: 1 CHM3400 - Lecture 3 – Jan 10 Maxwell distribution laws and molecular collisions (Chapter 2 p. 25-31) If we want to determine the velocity distribution for a large number of particles, we need to rely on a statistical treatment. The Maxwell-Boltzmann distribution (based on classical statistical mechanics) gives a representation of the velocity distribution for an ensemble of particles. T k E B kin 2 3 = 2 2 1 v m In the previous lecture, we saw that the temperature of a gas is related to the average kinetic energy of the particles (root-mean-square velocity ): 2 Maxwell-Boltzmann distribution x B x B dv T k mv T k m N dN ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = 2 exp 2 2 2 / 1 π Fraction of particles moving at velocity v x + d v x along direction x ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = T k mc T k m c c f B B 2 exp 2 4 ) ( 2 2 / 3 2 π π Can re-write this for the general velocity (directionless) c : Probability function (i.e., number/fraction of molecules) Velocity c Mass of particle Absolute temperature Velocity c 3 Understanding the M-B function ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = T k mc T k m c c f B B 2 exp 2 4 ) ( 2 2 / 3 2 π π N 2 @ 300 K 200 400 600...
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## This note was uploaded on 05/29/2011 for the course CHM 3400 taught by Professor Seabra during the Spring '08 term at University of Florida.

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110110 - 1 CHM3400 Lecture 3 – Jan 10 Maxwell...

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